In this section, we present several numerical examples to demonstrate the performance of the proposed adaptive multiresolution UWDG schemes for solving the KdV equation and the ZK equation. For the time discretization, we employ the third-order implicit-explicit (IMEX) Runge-Kutta (RK) method in [1]}. All adaptive calculations are obtained by \(k=2\) , unless otherwise stated. The maximum mesh level \(N\)  is set to be 8. \(\textrm {DoF}=\textrm {dim}({\bf V})\)  refers to the number of Alpert's multiwavelets basis functions in the adaptive grids. The coarsening threshold \(\eta \)  is taken to be \(\epsilon /10\)  with \(\epsilon \)  to be the refinement threshold [2]}.
